Describe the method to Determination of wavelength of light by diffraction grating using spectrometer

To determine the wavelength of light using a diffraction grating and a spectrometer, follow these steps:

1. Setup the Apparatus:

   • Spectrometer: Ensure it’s properly calibrated and aligned.
   • Diffraction Grating: Place it securely in the spectrometer’s optical path. The grating should be mounted such that light can pass through or reflect off its surface.

2. Align the Light Source:

   • Position a monochromatic light source (like a sodium lamp or a laser) so that its light is directed at the diffraction grating. The light should be parallel to the grating lines.

3. Adjust the Spectrometer:

   • Set the spectrometer to a suitable angle to observe the diffraction pattern. Typically, you will start with the spectrometer’s telescope aligned to view the zero-order (central) maximum.

4. Measure the Angles:

   • Identify the diffracted orders on the spectrometer’s scale. The diffraction grating will produce multiple maxima (bright lines) at specific angles. Measure the angle of the first-order maximum ($\theta_1$) and if needed, higher-order maxima ($\theta_2$, etc.).

5. Record the Diffraction Grating Details:

   • Note the number of lines per millimeter (or per meter) on the diffraction grating, which is its grating constant $d$ (the distance between adjacent lines).

6. Apply the Diffraction Grating Equation:

   • Use the diffraction grating equation to calculate the wavelength of the light: $$d \sin(\theta) = m \lambda$$ where:
     • $d$ is the grating spacing (inverse of lines per unit length),
     • $\theta$ is the angle of the diffracted maximum,
     • $m$ is the order of the maximum (1 for first order, 2 for second order, etc.),
     • $\lambda$ is the wavelength of the light.

7. Calculate the Wavelength:

   • Rearrange the equation to solve for $\lambda$: $$\lambda = \frac{d \sin(\theta)}{m}$$
   • Plug in the values for $d$, $\theta$, and $m$ to find the wavelength.

8. Verify and Repeat:

   • Repeat the measurement for different orders of maxima to ensure accuracy and consistency in the calculated wavelength.

By following these steps, you can accurately determine the wavelength of light using a diffraction grating and a spectrometer.